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Mixed finite element methods for generalized Forchheimer flow in porous media
Author(s) -
Park EunJae
Publication year - 2005
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.20035
Subject(s) - mathematics , uniqueness , porous medium , finite element method , nonlinear system , flow (mathematics) , partial differential equation , mathematical analysis , darcy's law , momentum (technical analysis) , partial derivative , porosity , geometry , thermodynamics , physics , materials science , composite material , finance , quantum mechanics , economics
Mixed finite element methods are analyzed for the approximation of the solution of the system of equations that describes the flow of a single‐phase fluid in a porous medium in ℝ d , d ≤ 3, subject to Forchhheimer's law—a nonlinear form of Darcy's law. Existence and uniqueness of the approximation are proved, and optimal order error estimates in L ∞ ( J ; L 2 (Ω)) and in L ∞ ( J ; H (div; Ω)) are demonstrated for the pressure and momentum, respectively. Error estimates are also derived in L ∞ ( J ; L ∞ (Ω)) for the pressure. © 2004 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2005